In the spirit of STNG's "The Chase": DNA data storage

Hard disks are expensive and require a constant supply of electricity, while even the best “no-power” archiving materials such as magnetic tape degrade within a decade. This is a growing problem in the life sciences, where massive volumes of data — including DNA sequences — make up the fabric of the scientific record.

“We already know that DNA is a robust way to store information because we can extract it from wooly mammoth bones, which date back tens of thousands of years, and make sense of it,” explains Nick Goldman of EMBL-EBI. “It’s also incredibly small, dense and does not need any power for storage, so shipping and keeping it is easy.”

However, in general, Trek seems to go for the scifi trope of "crystals" being a powerful no-power data storage medium capable of defying time for aeons. Biological, potentially self-repairing data media are another way to go, but not the preferred one. Although those gel-pack computing aids from VOY might be an experiment on that other path.